Question

A plane is flying at an elevation of 32000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 22∘. Find the distance between the plane and the airport. Find the distance between a point on the ground directly below the plane and the airport.

Answer 1

Answer:x=79,202.77 ft

Explanation:

Given

plane is at a height of 32000 ft

angle of depression is $22^{\circ}$

let x the distance between the point directly below the plane and airport be x

from diagram

$\tan (22)=\frac{height}{x}$

$\tan (22)=\frac{32000}{x}$

x=79,202.77 ft

distance between plane and airport

$\sin (22)=\frac{32000}{h}$

$h=\frac{32000}{\sin (22)}$

h=85,422.94 ft